DataSheet1_A Reduced-Order RNN Model for Solving Lyapunov Equation Based on Efficient Vectorization Method.xlsx

With the trend of electronization of the power system, a traditional serial numerical algorithm is more and more difficult to adapt to the demand of real-time analysis of the power system. As one of the important calculating tasks in power systems, the online solution of Lyapunov equations has attracted much attention. A recursive neural network (RNN) is more promising to become the online solver of the Lyapunov equation due to its hardware implementation capability and parallel distribution characteristics. In order to improve the performance of the traditional RNN, in this study, we have designed an efficient vectorization method and proposed a reduced-order RNN model to replace the original one. First, a new vectorization method is proposed based on the special structure of vectorized matrix, which is more efficient than the traditional Kronecker product method. Second, aiming at the expanding effect of vectorization on the problem scale, a reduced-order RNN model based on symmetry to reduce the solution scale of RNN is proposed. With regard to the accuracy and robustness, it is proved theoretically that the proposed model can maintain the same solution as that of the original model and also proved that the proposed model is suitable for the Zhang neural network (ZNN) model and the gradient neural network (GNN) model under linear or non-linear activation functions. Finally, the effectiveness and superiority of the proposed method are verified by simulation examples, three of which are standard examples of power systems.

随着电力系统电子化的发展趋势，传统串行数值算法愈发难以适配电力系统实时分析的需求。作为电力系统中的重要计算任务之一，李雅普诺夫方程（Lyapunov equations）的在线求解受到了广泛关注。递归神经网络（RNN）凭借其硬件实现能力与并行分布特性，有望成为李雅普诺夫方程的在线求解器。为改善传统RNN的性能，本研究设计了一种高效的向量化方法，并提出了一种降阶RNN模型以替代原始模型。首先，基于向量化矩阵的特殊结构，本文提出了一种新型向量化方法，其效率优于传统的克罗内克积（Kronecker product）方法。其次，针对向量化对问题规模的扩增效应，本文提出了一种基于对称性的降阶RNN模型，以缩减RNN的求解规模。在精度与鲁棒性方面，本文从理论上证明了所提模型可保持与原始模型一致的求解效果，同时证明了该模型适用于线性或非线性激活函数下的张神经网络（ZNN）与梯度神经网络（GNN）模型。最后，通过仿真算例验证了所提方法的有效性与优越性，其中3个为电力系统标准算例。